Problem: There is a light source on the plane. This source is so small that it can be represented as point. The light source is moving from point (a, s_y) to the (b, s_y) (s_y < 0) with speed equal to 1 unit per second. The trajectory of this light source is a straight segment connecting these two points. 

There is also a fence on OX axis represented as n segments (l_i, r_i) (so the actual coordinates of endpoints of each segment are (l_i, 0) and (r_i, 0)). The point (x, y) is in the shade if segment connecting (x,y) and the current position of the light source intersects or touches with any segment of the fence.

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You are given q points. For each point calculate total time of this point being in the shade, while the light source is moving from (a, s_y) to the (b, s_y).

Input

First line contains three space separated integers s_y, a and b (-10^9 ≤ s_y < 0, 1 ≤ a < b ≤ 10^9) — corresponding coordinates of the light source.

Second line contains single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — number of segments in the fence.

Next n lines contain two integers per line: l_i and r_i (1 ≤ l_i < r_i ≤ 10^9, r_{i - 1} < l_i) — segments in the fence in increasing order. Segments don't intersect or touch each other.

Next line contains single integer q (1 ≤ q ≤ 2 ⋅ 10^5) — number of points to check.

Next q lines contain two integers per line: x_i and y_i (1 ≤ x_i, y_i ≤ 10^9) — points to process.

Output

Print q lines. The i-th line should contain one real number — total time of the i-th point being in the shade, while the light source is moving from (a, s_y) to the (b, s_y). The answer is considered as correct if its absolute of relative error doesn't exceed 10^{-6}.

Example

Input

-3 1 6
2
2 4
6 7
5
3 1
1 3
6 1
6 4
7 6


Output

5.000000000000000
3.000000000000000
0.000000000000000
1.500000000000000
2.000000000000000

Note

  * The 1-st point is always in the shade; 
  * the 2-nd point is in the shade while light source is moving from (3, -3) to (6, -3); 
  * the 3-rd point is in the shade while light source is at point (6, -3). 
  * the 4-th point is in the shade while light source is moving from (1, -3) to (2.5, -3) and at point (6, -3); 
  * the 5-th point is in the shade while light source is moving from (1, -3) to (2.5, -3) and from (5.5, -3) to (6, -3); 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
long double ls[200005];
long double rs[200005];
int prefix[200005];
int N;
long double query(long double x) {
  auto it = std::upper_bound(ls, ls + N, x);
  if (it == ls) return 0;
  it--;
  int i = it - ls;
  return prefix[i] + std::min(x, rs[i]) - ls[i];
}
int main() {
  int S, A, B;
  scanf("%d %d %d", &S, &A, &B);
  scanf("%d", &N);
  for (int i = 0; i < N; i++) {
    int L, R;
    scanf("%d %d", &L, &R);
    ls[i] = L, rs[i] = R;
    prefix[i + 1] = prefix[i] + R - L;
  }
  int Q;
  scanf("%d", &Q);
  for (int i = 0; i < Q; i++) {
    int X, Y;
    scanf("%d %d", &X, &Y);
    long double tmp =
        query((long double)((int64_t)B * Y - (int64_t)S * X) / (Y - S)) -
        query((long double)((int64_t)A * Y - (int64_t)S * X) / (Y - S));
    printf("%.10lf\n", (double)(tmp / Y * (Y - S)));
  }
  return 0;
}